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Discrete Mathematics – Q&A

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identity , equal , equivalent --- are used in mathematics . are identity and equal both same ?? if same then we can put = sign in every identity . but Identities are sometimes indicated by the triple bar symbol ≡ instead of = ------ what does it mean?? if we use the triple bar ≡ , then it becomes equivalent .now we can say identities are sometimes equivalent. is it true? it becomes confusing .please explain with example . please help to learn the actual concept.
For each of the following words: if it is a sentence in the grammar, draw its derivation
tree; if it is not a sentence, explain carefully how you know that it is not a sentence.

(i) a/b − c/d ∗ e + f
A relation R defined on a set S is said to be ………… if b R a
∀a,b∈S
.
a. transitive
b. reflexive
c. symmetric
d. none of the above
Who has developed the concept of congruence and when he has developed the concept?
Who has developed the concept of congurences and when has he developed the concept?
who has developed the concept of congurences and when he developed the concept?
Q. where the concept of a function first arose? Also find that who has arosed this concept? Also describe How this concept was first used?
Use Mathematical Induction to prove the following:
(i) 1
2 + 22 + 32 + … + n
2 =
Write a sequence formula?????

1,4,9,16,25,.........
without using truth table prove that
¬(p↔q) and ¬p↔q are logically equivalent.
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